Identifying Transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

Front

What are the four main types of transformations?

Back

Translation, Reflection, Rotation, Dilation.

Front

Define Translation.

Back

Translation is a transformation that moves every point of a shape the same distance in the same direction.

Front

Define Reflection.

Back

Reflection is a transformation that flips a shape over a line, creating a mirror image.

Front

Define Rotation.

Back

Rotation is a transformation that turns a shape around a fixed point at a certain angle.

Front

Define Dilation.

Back

Dilation is a transformation that changes the size of a shape but keeps its proportions the same.

Front

What is the effect of a translation of (x, y) → (x + a, y + b)?

Back

It moves the shape 'a' units horizontally and 'b' units vertically.

Front

What is the effect of a reflection over the x-axis?

Back

It changes the sign of the y-coordinate of each point (x, y) to (x, -y).

Front

What is the effect of a rotation of 90 degrees counterclockwise around the origin?

Back

It transforms the point (x, y) to (-y, x).

Front

How do you identify the quadrant of a point with coordinates (x, y)?

Back

Quadrant I: x > 0, y > 0; Quadrant II: x < 0, y > 0; Quadrant III: x < 0, y < 0; Quadrant IV: x > 0, y < 0.